Civil Engineering Reference
In-Depth Information
been extensively examined. In the absence of further research, the geomet-
ric mean of the pair of ground motions,
S
a
g.m
.
, at the geometric mean of the
two periods is used as the IM parameter as recommended by Baker and
Cornell (2006c).
The 39 pairs of records were applied twice to the model, once with the
ground motion records oriented along one principal direction, and then
again with the records rotated 90 degrees. This resulted in 78 IDA curves.
The use of pairs of ground motions in IDA using 3D models for the multi-
degree of freedom bridges with single column bents studied resulted in
'waving' behaviour with some points of structural resurrection (i.e., the
structure resists seismic forces at higher IM values after a collapse at a lower
IM value; see Vamvatsikos and Cornell, 2002, for the more details). This is
because the timing, details and frequency contents of the ground motions
have a signifi cant effect on the seismic response and when the records are
applied in pairs the complexity of the seismic response increases even more.
Therefore the IDA analyses were performed using very small increments
of IM values to determine the maximum seismic demands at each intensity
level. The increments were considered as 5% of the spectral acceleration at
the MCE level (e.g., 0.0065 (
g
) at
T
1.09 s). The IDA analyses were con-
tinued up to twice the intensity level at which the fi rst global dynamic
instability (collapse) was observed, due to possible structural resurrection.
The percentiles of the IDA results were determined using the IM|DM
and DM|IM approaches. For the IM|DM method the lowest spectral accel-
eration at which the global dynamic instability occurs is determined as the
collapse capacity for each record and subsequently the percentiles are
determined. For complex IDA curves (i.e., due to waiving and resurrection
behaviour) the use of the IM|DM percentiles can be conservative. The
DM|IM percentiles are determined based on the percentiles of the drift
ratios at each IM level. The DM|IM percentiles for such cases can provide
more reasonable predictions of the IDA percentiles. It should be noted that
where the IDA curves do not exhibit waving and structural resurrection
behaviours the line connecting the x% percentiles of DM|IM is typically
the same as the one connecting the (100
=
x
)% percentiles of IM|DM
(Vamvatsikos and Cornell, 2004). The DM|IM percentile curves are shown
in Fig. 21.9. In Table 21.4 more details of the IDA results determined for
different damage states are presented. Some researchers have expressed
their concerns about the scaling of the pairs of ground motion and the
choice of a scale factor for the orthogonal component of a ground motion
(e.g., Baker and Cornell, 2006c). In the ATC-63 provisions (ATC-63, 2008)
concern is expressed about the results from the 3D analysis being conser-
vative. Because ground motions records are applied in pairs in three-
dimensional nonlinear dynamic analyses, the resulting behaviour from each
ground motion component is coupled. On the other hand the use of 2D
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